Structure of ${}^{23}$Al from the one-proton breakup reaction and astrophysical implications

The ground state of the proton-rich nucleus ${}^{23}$Al has been studied by one-proton removal on a carbon target at about 50 MeV/nucleon using the EXOGAM $+$ SPEG experimental setup at GANIL. Longitudinal momentum distributions of the ${}^{22}$Mg breakup fragments, inclusive and in coincidence with $\gamma$ rays de-exciting the residues, were measured. The ground-state structure of ${}^{23}$Al is found to be a configuration mixing of a $d$-orbital valence proton coupled to four core states—0${}_{\text{gs}}^{+}$, 2${}_1^{+}$, 4${}_1^{+}$, 4${}_2^{+}$. We confirm the ground state spin and parity of ${}^{23}$Al as $J^{\pi }=5/2^{+}$. The measured exclusive momentum distributions are compared with extended Glauber model calculations to extract spectroscopic factors and asymptotic normalization coefficients (ANCs). The spectroscopic factors are presented in comparison with those obtained from large-scale shell model calculations. We determined the asymptotic normalization coefficient of the nuclear system ${}^{23}$Al${}_{\text{gs}}$ $\to$ ${}^{22}$Mg(0${}^{+}$) $+$ $p$ to be $C_{d_{5/2}}^2{(}^{23}{\text{Al}}_{\text{gs}})=(3.90\pm 0.44)\times {10}^3{\text{fm}}^{-1}$, and used it to infer the stellar reaction rate of the direct radiative proton capture ${}^{22}$Mg($p$,$\gamma$)${}^{23}$Al. Astrophysical implications related to ${}^{22}$Na nucleosynthesis in ONe novae and the use of one-nucleon breakup at intermediate energies as an indirect method in nuclear astrophysics are discussed.

Figure 1

Experimental inclusive momentum distribution of ${}^{22}$Mg cores (points), in the center-of-mass frame, compared with a theoretical distribution calculated for the $2s_{1/2}$ single-particle orbital (dashed curve, arbitrary units) and with a calculated inclusive momentum distribution using the $1d_{5/2}$ orbital and the theoretical spectroscopic factors (full curve, absolute normalization) obtained from large-scale shell model calculations (see text).

Figure 2

Doppler-corrected $\gamma$-ray spectrum in coincidence with identified ${}^{22}$Mg residues in SPEG. The inset shows the levels and transitions in ${}^{22}$Mg core fragments.

Figure 3

Experimental exclusive momentum distributions determined in the center-of-mass frame for ${}^{22}$Mg residues corresponding to ${}^{23}$Al ground state configuration mixing. Comparison with calculations using spectroscopic factors from fit (see text). In the second panel from the top the full (dashed) curve is associated with calculations that include (exclude) the contribution of the ${|}^{22}\text{Mg}\left(2^{+}\right)\otimes \pi 2s_{1/2}\rangle$. The dot-dashed curve is the calculated momentum distribution of a pure $s$ wave. Shaded areas correspond to $1\sigma$ deviation in the spectroscopic amplitudes. The uncertainties contain the statistical errors and those from the $\gamma$-ray efficiencies.

Figure 4

Experimental inclusive momentum distribution (points) in the center-of-mass reference frame compared with the calculated one using the fitted spectroscopic factors (full curve). The lower curves present the contributions of each of the configurations identified, labeled by the core states. The full (dashed) curve is associated with the full calculation that includes (excludes) the contribution of the ${|}^{22}\text{Mg}\left(2^{+}\right)\otimes \pi 2s_{1/2}\rangle$. Same for the curve labeled 2${}^{+}$.